Transport of hydrogen isotopes through interlayer spacing in van der Waals crystals


Atoms start behaving as waves rather than classical particles if confined in spaces commensurate with their de Broglie wavelength. At room temperature this length is only about one ångström even for the lightest atom, hydrogen. This restricts quantum-confinement phenomena for atomic species to the realm of very low temperatures1,2,3,4,5. Here, we show that van der Waals gaps between atomic planes of layered crystals provide ångström-size channels that make quantum confinement of protons apparent even at room temperature. Our transport measurements show that thermal protons experience a notably higher barrier than deuterons when entering van der Waals gaps in hexagonal boron nitride and molybdenum disulfide. This is attributed to the difference in the de Broglie wavelengths of the isotopes. Once inside the crystals, transport of both isotopes can be described by classical diffusion, albeit with unexpectedly fast rates comparable to that of protons in water. The demonstrated ångström-size channels can be exploited for further studies of atomistic quantum confinement and, if the technology can be scaled up, for sieving hydrogen isotopes.

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Fig. 1: Devices for testing interlayer permeation of protons.
Fig. 2: Proton permeation for different devices and geometries.
Fig. 3: Dependence of activation energy on channel length.
Fig. 4: Isotope effect for interlayer transport.


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The authors acknowledge support from the Lloyd’s Register Foundation, EPSRC - EP/N010345/1, the European Research Council ARTIMATTER project - ERC-2012-ADG and from Graphene Flagship. M.L.-H. acknowledges a Leverhulme Early Career Fellowship.

Author information




A.K.G. designed the project and directed it with help of S.H. and M.L.-H. S.H. fabricated devices, K.G. performed transport measurements. M.L.-H. and S.H. carried out data analyses. A.R. and S.J.H. performed TEM and SEM measurements. F.M.P., M.N.-A. and T.H. provided theoretical support. M.L.-H., I.V.G., S.H. and A.K.G. wrote the manuscript. All co-authors took part in discussing results.

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Correspondence to S. Hu or A. K. Geim or M. Lozada-Hidalgo.

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Hu, S., Gopinadhan, K., Rakowski, A. et al. Transport of hydrogen isotopes through interlayer spacing in van der Waals crystals. Nature Nanotech 13, 468–472 (2018).

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